Which turned out, from my google researches, to be the 'proper' way to do it:
“Most Russians celebrate New Year's Eve with their families and close friends. The celebration usually starts one or two hours before midnight and the common tradition is to "say farewell to the old year" by remembering most important events of the last twelve months. At five minutes to twelve most of the people watch the president's speech on TV or watch popular New Year TV shows ("Goluboy Ogonek"). There is a tradition to listen to the Kremlin clock bell ('Kuranty') ringing twelve times on the radio or on TV. During these last 12 seconds of the year people keep silence and make their secret wishes for the next year.”
Which is exactly what we did. Well not the silences and the wishes thing, And to be honest we didn't watch the TV show, we gaped at it. It was all glitter, flashing coloured lights, bling, celebs, loudness, singalong songs, over-acting and gurning for the camera, and endless over-the-top theatrical gestures. I've stolen an image from the brilliant English Russia website, because I was too stunned to photo the TV. And in fact, for a great inside story and more images, go to their blog and read Happy Fake Year.